Hypothesis Testing MCQs 2026

The test statistic measures how many standard errors the sample estimate is from

1. Athe confidence level✓
2. Bthe chi-square df✓
3. Cthe value specified under H0✓
4. Dthe population size N only✓

Directional hypothesis after data peeking

1. Ais always valid✓
2. Binflates Type I error if not pre-specified✓
3. Clowers α automatically✓
4. Dhas no effect on inference✓

Equivalence testing aims to show

1. Aμ differs from μ0 by any amount✓
2. Bonly p > 0.05✓
3. Cparameter lies within a pre-specified practical equivalence margin✓
4. Donly chi-square fit✓

A significance test is not valid if

1. An is large✓
2. Bα is 0.05✓
3. Ct is used✓
4. Ddata are not collected under a designed protocol (e.g., optional stopping without correction)✓

In court analogy, Type II error is like

1. Aconvicting innocent✓
2. Bannouncing α✓
3. Cacquitting a guilty person✓
4. Dcomputing SE✓

In court analogy, Type I error is like

1. Afreeing a guilty person✓
2. Bcollecting evidence✓
3. Cconvicting an innocent person✓
4. Dsetting confidence level✓

Reporting only p-value without effect size

1. Ais always best practice✓
2. Beliminates Type II error✓
3. Creplaces assumptions check✓
4. Dcan mislead when n is very large (tiny effects significant)✓

Permutation test p-value is obtained by

1. Acomparing observed statistic to distribution under random relabeling✓
2. Busing only z-tables always✓
3. Cassuming π = 0.5 always✓
4. Dignoring the actual data✓

False discovery rate control is important when

1. Aonly one t-test is performed✓
2. Bonly descriptive stats are computed✓
3. Cmany hypotheses are screened (multiple testing)✓
4. Dcensus is conducted✓

For large samples, z and t critical values

1. Adiffer by factor of 2 always✓
2. Bt is always 0✓
3. Care nearly equal✓
4. Dz is always 3✓

Testing H0: μ = 0 with t-test, the numerator of t is

1. As only✓
2. Bσ²✓
3. Cp̂−π0✓
4. Dx̄ − 0✓

A borderline p-value near α suggests

1. Adefinitive proof of H0✓
2. Binconclusive evidence — consider larger n or effect size✓
3. Cno need for replication✓
4. Dautomatic rejection✓

β depends on

1. Aonly the p-value observed✓
2. Bonly the confidence level✓
3. Ctrue parameter value, sample size, α, and effect size✓
4. Donly chi-square df alone✓

α = 0.05 corresponds to

1. A5% power✓
2. B5% Type I error if H0 is true and test assumptions hold✓
3. C95% Type II error always✓
4. D5% confidence coefficient✓

Likelihood ratio test compares

1. Aonly sample means visually✓
2. Bonly contingency margins✓
3. Conly index numbers✓
4. Dmaximized likelihood under H0 vs unrestricted model✓

Standard error under H0 for one-sample mean z-test uses

1. As/√n in denominator with H0 value in standardized form✓
2. Bπ0(1−π0)✓
3. Cχ² df✓
4. Dσ/√n with μ0 in numerator setup✓

One-tailed Ha: μ > μ0 rejects when

1. Atest statistic is negative large✓
2. Bz or t exceeds positive critical value✓
3. Cp-value > α✓
4. Dχ² is small✓

Hypothesis test requires

1. Aassumptions about sampling, distribution, and independence✓
2. Bno assumptions if n > 5✓
3. Conly graphical presentation✓
4. Donly census data✓

Nonparametric alternative to two independent samples

1. AMann–Whitney U (Wilcoxon rank-sum) test✓
2. Bpaired t-test✓
3. Cgoodness of fit only✓
4. DF-test on means✓

Nonparametric alternative to paired t when differences are non-normal

1. Az-test on proportions only✓
2. BWilcoxon signed-rank test✓
3. Cone-way ANOVA✓
4. Dchi-square independence✓

Robustness of t-test means

1. Anever works without n > 10000✓
2. Bmoderate non-normality with adequate n often still valid✓
3. Crequires chi-square population✓
4. Deliminates Type I error✓

Relationship between CI and two-sided test at α

1. Avalues inside (1−α)100% CI are not rejected as μ0✓
2. BCI always narrower than test region✓
3. Cunrelated procedures✓
4. DCI replaces need for assumptions✓

If p-value = 0.08 at α = 0.05, decision is

1. Areject H0✓
2. Bfail to reject H0✓
3. Cprove Ha✓
4. Dset β = 0.08✓

If p-value = 0.03 at α = 0.05, decision is

1. Areject H0✓
2. Bfail to reject H0✓
3. Caccept H0 as proven✓
4. Dincrease α to 0.01✓

Rejection rule for two-tailed t-test at α = 0.05

1. At_obs > 0 only✓
2. B|t_obs| < t_{0.025}✓
3. C|t_obs| > t_{0.025, df}✓
4. Duse χ²_{0.05}✓

A test statistic is standardized to compare

1. Aonly sample size✓
2. Bonly confidence width✓
3. Conly non-sampling error✓
4. Dobserved discrepancy from H0 to its null distribution✓

Bonferroni correction adjusts α when

1. Aonly one test is run✓
2. Bonly for chi-square✓
3. Csample size is infinite✓
4. Dmultiple hypotheses are tested simultaneously✓

Effect size for two means might use

1. ACohen's d = (x̄1−x̄2)/sp✓
2. Bonly p-value✓
3. Conly α✓
4. Donly chi-square statistic✓

Levene's test assesses

1. Aindependence of proportions only✓
2. Bgoodness of fit to Poisson✓
3. Ccontingency independence only✓
4. Dhomogeneity of variances without strong normality assumption✓

F-test for equality of two variances is

1. Asensitive to non-normality — use with caution✓
2. Balways preferred to Levene test✓
3. Cidentical to t-test on means✓
4. Da chi-square test on means✓

Pooled two-sample t-test assumes

1. Apaired observations✓
2. Bmultistage sampling only✓
3. Conly categorical data✓
4. Dequal population variances (σ1² = σ2²)✓

Test of H0: μ1 − μ2 = 0 with unequal variances uses

1. Apooled t always without checking✓
2. BWelch's t-test with adjusted degrees of freedom✓
3. Cz with π0✓
4. Dchi-square goodness of fit✓

As df → ∞, t-distribution approaches

1. Achi-square✓
2. BF with 1 df✓
3. Cstandard normal✓
4. Duniform✓

The t-distribution has

1. Alighter tails always✓
2. Bheavier tails than the standard normal✓
3. Cno variance✓
4. Ddf = 0 always✓

Paired t-test df equal

1. An1 + n2 − 2✓
2. Bk − 1✓
3. Cn − 1 where n is number of pairs✓
4. D2n✓

Conditions for z-test on proportion include

1. An = 1 always✓
2. Bnormal population for each individual✓
3. Cnp0 and n(1−p0) sufficiently large under H0✓
4. Dequal variances✓

z-test for H0: π = π0 uses

1. At with n−1✓
2. Bχ² with k−1✓
3. Conly paired differences✓
4. Dz = (p̂−π0)/√[π0(1−π0)/n]✓

Choosing one-sided vs two-sided test should be

1. Achosen after seeing direction of difference to maximize significance✓
2. Balways two-sided for proportions only✓
3. Cignored in CSS exams✓
4. Ddecided before seeing data based on research question✓

One-sided test at α has

1. Aα/2 in each tail✓
2. Bzero power✓
3. Call α in one tail of the null distribution✓
4. Dno critical value✓

Failing to reject H0

1. Adoes not prove H0 is true — may lack power✓
2. Bproves H0 is true✓
3. Cproves Ha is false✓
4. Dimplies p = 1✓

A very small p-value suggests

1. AH0 is certainly true✓
2. Bthe sample size is too small always✓
3. Cα should be raised✓
4. Dthe observed data are unlikely if H0 were true✓

Practical significance refers to

1. Aonly p < 0.05✓
2. Bonly Type I error✓
3. Cwhether an effect is large enough to matter in context✓
4. Donly chi-square df✓

Statistical significance at α = 0.05 means

1. Athe effect is practically important✓
2. BH0 is proven true✓
3. Cβ = 0.05✓
4. Dp-value < 0.05 under the conducted test✓

Decreasing α from 0.05 to 0.01

1. Aincreases power always✓
2. Bincreases Type II error probability in many settings✓
3. Creduces Type I error but lowers power✓
4. Deliminates need for n✓

Increasing sample size while effect size fixed generally

1. Aincreases power✓
2. Bincreases β always✓
3. Cdecreases power✓
4. Dleaves power unchanged always✓

Critical region is

1. Aalways the middle of the distribution✓
2. Bthe set of test statistic values leading to rejection of H0✓
3. Cthe confidence interval✓
4. Dthe sample mean only✓

Test statistic for two-sample z on proportions is

1. At with n1+n2−2 always✓
2. Bz = (p̂1−p̂2)/SE(p̂1−p̂2)✓
3. Cχ² only✓
4. DF only✓

Two-sample t-test (independent) tests

1. Aequality of two population means✓
2. Bequality of variances only always✓
3. Conly proportions✓
4. Donly goodness of fit✓

Paired t-test analyzes

1. Atwo independent groups only✓
2. Bcontingency tables only✓
3. Cdifferences within matched pairs✓
4. Donly proportions✓

One-sample t-test for mean is used when

1. Aσ is known always✓
2. Bonly for paired data✓
3. Conly for chi-square✓
4. Dσ is unknown, data are from normal population (or large n by robustness)✓

One-sample z-test for mean is appropriate when

1. Aσ is always unknown and n = 5✓
2. Bσ is known and population is normal or n is large✓
3. Cpopulation is always skewed with n = 10✓
4. Donly for proportions✓

A two-tailed z-test for H0: μ = μ0 uses critical values

1. A±z_{α/2}✓
2. Bz_α only on one side✓
3. Ct_{α/2} always✓
4. Dχ²_{α}✓

Power of a test is

1. A1 − β, the probability of correctly rejecting a false H0✓
2. Bthe probability of Type I error✓
3. Cthe p-value✓
4. Dthe margin of error✓

Reject H0 when p-value

1. Aexceeds α✓
2. Bis less than α (for the chosen test)✓
3. Cequals 1 always✓
4. Dequals the confidence level✓

The p-value is

1. Athe probability, assuming H0 is true, of obtaining a test statistic at least as extreme as observed✓
2. Bthe probability H0 is true✓
3. Cthe same as α always✓
4. Dthe confidence level✓

The significance level α is

1. Athe probability of Type II error✓
2. Bthe maximum acceptable probability of Type I error✓
3. Cthe p-value always✓
4. Dthe power of the test✓

Type II error is

1. Arejecting true H0✓
2. Bsetting confidence level✓
3. Cchoosing sample size only✓
4. Dfailing to reject H0 when H0 is false✓

Type I error is

1. Afailing to reject a false H0✓
2. Brejecting H0 when H0 is true✓
3. Caccepting Ha when Ha is false only✓
4. Dcomputing a CI✓

The alternative hypothesis Ha may be

1. Aone-sided or two-sided depending on the research question✓
2. Balways two-sided only✓
3. Calways μ = 0✓
4. Dalways the confidence interval✓

The null hypothesis H0 typically represents

1. Aa statement of no effect, no difference, or a specified parameter value✓
2. Bthe research claim always✓
3. Cthe alternative only✓
4. Dthe p-value✓